By applying mild shock through their bodies, often by a stun gun or electrical outlet, a fluffy pony can be rendered into temporary trance-like state where they are open to mental suggestion. This is when a human owner will speak to the fluffy and either order it to forget certain events, act a certain way, stop a certain behavior, or even make them think they are somebody or something else. The most common use for resetting a fluffy is when a human abuses and tortures a fluffy and makes it forget that the human abused them. That makes the fluffy think they always had those injuries before or never had any of their now missing limbs. Once the reset is done the fluffy is usually none the wiser.
Resetting does have it's limits though. Reseting a fluffy and telling it to do something it normally wouldn't know how to do often doesn't work. For example if you shock your fluffy and tell it to speak French it won't magically know the language, at best it will speak french sounding gibberish or if you tell it act like an animal it has never seen before it will simply say that it is the animal you mentioned. Caution is advised though as repeated shocks can cause brain damage and eventually leave the pony effectively brain dead.
Certain facts or events are too ingrained or traumatizing in the fluffy's being to stay forgotten. If something brings that fact or memory to their attention, sometimes their previous memories can come flooding right back and the effects of the reset are lost.
Fluffy resets started during the time where an old head canon had fluffies with computer chips in their brains which influenced their behavior and gave them the ability to speak and understand English. The electrical shock is what would reset the fluffy's brain chip which is what made them re-programmable. This head canon has since stopped being accepted as the common reason why fluffies behave the way they do and that is part of why fluffy resets aren't as common as they used to be.
Additionally, the reset, if it functions correctly, is essentially a deus-ex machina in-universe, allowing most conflicts to be solved with a simple reset, if a fluffy is a brat, just reset it, if a fluffy is traumatized, just reset it, if a fluffy misses its former owner, just reset it. As resets have the potential to remove most conflicts, they have been little used recently, and when they are used, they typically involve a failed reset, rather than a successful one.